Question

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 4} and B = {5, 6}, then show that A – B = A ∩B| = B|-A| .

Answer 1

Answer:

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B)

′

=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}

=ϕ

A

′

∩B

′

=(U−A)n(U−B)

={3,4,6}n{1,2,7}

=ϕ

Hence (A∪B)

′

=A

′

∩B

′

.